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## Mildly interesting rule

For discussion of other cellular automata.

### Mildly interesting rule

This is a 6-state rule I came up with while messing about. It's a little hard to express the ideas behind it in words, so here's a ruletable:

`n_states:6neighborhood:Mooresymmetries:permutevar a={3,5}var b={3,5}var c={3,5}var d={3,5}var e={3,5}var f={3,5}var g={3,5}var h={3,5}var j={0,1,2,4}var k={0,1,2,4}var l={0,1,2,4}var m={0,1,2,4}var n={0,1,2,4}var o={0,1,2,4}var p={0,1,2,4}var q={0,1,2,4}var s={0,1,2,3,4,5}var t={0,1,2,3,4,5}var u={0,1,2,3,4,5}var v={0,1,2,3,4,5}var w={0,1,2,3,4,5}var x={0,1,2,3,4,5}var y={0,1,2,3,4,5}var z={0,1,2,3,4,5}0,1,0,0,0,0,0,0,0,40,4,0,0,0,0,0,0,0,50,5,0,0,0,0,0,0,0,00,a,b,c,0,0,0,0,0,10,a,b,c,d,e,f,0,0,10,a,b,c,d,e,f,g,h,11,s,t,u,v,w,x,y,z,22,s,t,u,v,w,x,y,z,33,s,t,u,v,w,x,y,z,04,s,t,u,v,w,x,y,z,05,s,t,u,v,w,x,y,z,0`

It's a highly kinetic rule, with stationary objects pretty much nonexistent. There is one common c/9 orthogonal spaceship, a large variety of c/3 diagonal spaceships and rakes, and, bizarrely, a /tiny/ 47c/183 diagonal forward rake:

`x = 3, y = 3, rule = aurora192.A\$2.A\$2A!`
Pteriforever

Posts: 37
Joined: April 10th, 2013, 9:43 pm

### Re: Mildly interesting rule

Nice looking rule!
It seems a bit difficult constructing spaceships though

A basic symmetric diagonal C/3
`x = 5, y = 5, rule = aurora192.2A2\$A2.2A\$A.A\$2.A!`

Which can be extended indefinitely
`x = 11, y = 11, rule = aurora198.2A2\$9.2A2\$6.2A2\$4.A2.2A\$4.A.A\$A5.A\$A.A\$2.A!`

`x = 15, y = 15, rule = aurora19\$12.2A2\$13.2A2\$10.2A2\$8.A2.2A\$8.A.A\$4.A5.A\$4.A.A\$A5.A\$A.A\$2.A!`

However the result is not always stable for example this one stabilizes into a rake after emitting a lot of random debris
`x = 21, y = 13, rule = aurora1918.2A2\$16.A2.2A\$16.A.A\$12.A5.A\$12.A.A\$8.A5.A\$8.A.A\$4.A5.A\$4.A.A\$A5.A\$A.A\$2.A!`

such as this P6 oscillator!
`x = 6, y = 7, rule = aurora19.A\$5.A\$3.A.A2\$3.A.A\$5.A\$.A!`

Some other stuff
`x = 29, y = 29, rule = aurora1926.2A2\$27.2A2\$24.2A2\$25.2A2\$22.2A2\$23.2A2\$20.2A2\$21.2A2\$18.2A2\$16.A2.2A\$16.A.A\$12.A5.A\$12.A.A\$8.A5.A\$8.A.A\$4.A5.A\$4.A.A\$A5.A\$A.A\$2.A!`

A P24
`x = 9, y = 5, rule = aurora193A3.3A2\$3.A.A2\$2.A3.A!`

I hope to be more active now that summer is nearer and my interest in CA has sparked again
Why is it called aurora19 by the way?

Hektor

Posts: 89
Joined: November 3rd, 2011, 2:37 pm

### Re: Mildly interesting rule

Hmm. I guess I just end up naming rules rather strange things sometimes.
Pteriforever

Posts: 37
Joined: April 10th, 2013, 9:43 pm

### Re: Mildly interesting rule

The common but bizarre forward rake mentioned above has two possible two cell predecessors: a state 1 cell with either a state 3 or 5 cell diagonally next to it, which is the minimum population for infinite growth possible. From this I attempted to find a minimal population quadratic growth.

`x = 29, y = 28, rule = aurora1927.A\$28.C9\$19.A\$20.C7\$10.A\$11.C7\$A\$.C!`

This is an 8 cell quadratic growth candidate, and it was the first one I found. It has some really interesting behavior but it is very chaotic, which means I haven't been able to run it much farther than a million generations. As I started posting this I found that the rightmost 2 cells could be removed to make a 6 cell quadratic growth candidate, but that one produces fewer rake and has a significant period where no new rakes are added (which does end around one million generations), which makes the long term growth rate for that 6 cell pattern uncertain. The 8 cell pattern does look like it will exhibit quadratic growth indefinitely, although it may still fail.

`x = 59, y = 14, rule = aurora1950.A\$49.C6\$.A\$C2\$17.A\$16.C\$58.A\$57.C!`

This is also an 8 cell quadratic growth pattern, but with this one it is very obvious that the pattern will continue to fill the grid. The engine produces rakes rather fast once it warms up, which would already be enough to make it exhibit quadratic growth. The rakes then become transformed into breeders themselves, and their intersection makes and interesting density gradient pattern. Either of the left two most 'duoplets' can be removed to achieve a 6 cell quadratic growth pattern, and this time it has no effect on the result. In fact, I just realized just now while typing that last sentence that all of the four left most cells are unnecessary, and only the rightmost two are needed. This gives a 4 cell quadratic growth, which I believe is minimal.
Sphenocorona

Posts: 480
Joined: April 9th, 2013, 11:03 pm

### Re: Mildly interesting rule

Very nice (: I really like how that last one looks.

And then there's this thing, where the output weirdly interacts, it's kinda hard to explain:

`x = 51, y = 41, rule = aurora1915\$22.A\$22.A\$20.2A8\$12.A\$12.A\$10.2A!`
Pteriforever

Posts: 37
Joined: April 10th, 2013, 9:43 pm

### Re: Mildly interesting rule

I also found this p12:

`x = 11, y = 17, rule = aurora196.A\$10.A\$8.A.A2\$8.A.A\$10.A\$6.A6\$A5.A2\$2.A.A2\$.2A.2A!`
Pteriforever

Posts: 37
Joined: April 10th, 2013, 9:43 pm

### Re: Mildly interesting rule

Apparently this is a rule that alternates between three different stages?
1) "Red stage": B1/D. All state 1 cells survive as state 2. Newborn cells are state 4.
2) "Orange stage": B1/D. All state 2 cells survive as state 3. All state 4 cells die. Newborn cells are state 5.
3) "Yellow stage": B368/S. All old cells die, new state 1 cells are born. (I don't think the B8 is really doing anything, it's very difficult to get that many state 3 or state 5 cells together.)

Definitely one of the more interesting B1-alternating rules I've seen… The 4-cell breeder in particular is impressive in that it's actually a "near-cubic growth" pattern: the main engine actually creates breeders rather than rakes! You can see a pseudo-3D "tetrahedral" picture emerge if you run it long enough.

Incidentally, due to the period-2 component found in B1 growth, adding more B1/D stages does some interesting things:
— With three stages, using B3 or even B4 for recycling stable cells is far too powerful. B5 allows a 2c/4 diagonal replicator but not much else, B6 is largely irrelevant, while B7 makes everything explode (!).
— With four stages, B3 for recycling is too weak to create much of anything. B36 shrinks marginally less slowly (and allows some small oscillators). B35 shrinks fairly slowly, B34 creates an explosive mess, B356 creates very beautiful fractal-like chaotic clouds of activity (with no particular structure emerging).

Tropylium

Posts: 406
Joined: May 31st, 2011, 7:12 pm
Location: Finland

### Re: Mildly interesting rule

`x = 4, y = 13, rule = auroraext4A2\$4A8\$4A2\$4A!`

Here's a replicator for that last one

EDIT: Actually no, that seems to have been a different rule o_o
Pteriforever

Posts: 37
Joined: April 10th, 2013, 9:43 pm

### Re: Mildly interesting rule

Here's aurora19plus.table for that last one:
`n_states:10neighborhood:Mooresymmetries:permutevar a={5,9}var b={a}var c={a}var d={a}var e={a}var f={a}var g={a}var h={a}var s={0,1,2,3,4,5,6,7,8,9}var t={s}var u={s}var v={s}var w={s}var x={s}var y={s}var z={s}#B1: phase 1-3 stable & halo cells > halo cells0,1,0,0,0,0,0,0,0,60,6,0,0,0,0,0,0,0,70,3,0,0,0,0,0,0,0,80,7,0,0,0,0,0,0,0,80,8,0,0,0,0,0,0,0,9#States 2, 4 will be haloed-in and cannot contribute to birth#B356: phase 4 cells > stable cells0,a,b,c,0,0,0,0,0,10,a,b,c,d,e,0,0,0,10,a,b,c,d,e,f,0,0,1#Stable cells die at phase 41,s,t,u,v,w,x,y,z,22,s,t,u,v,w,x,y,z,33,s,t,u,v,w,x,y,z,44,s,t,u,v,w,x,y,z,55,s,t,u,v,w,x,y,z,0#Halo cells die after 1 gen6,s,t,u,v,w,x,y,z,07,s,t,u,v,w,x,y,z,08,s,t,u,v,w,x,y,z,09,s,t,u,v,w,x,y,z,0`

A skew triplet seems to be explosive:
`x = 3, y = 2, rule = aurora19plus.2A\$A!`

Smallish patterns can frequently die off though, e.g. this one after 2045 generations:
`x = 15, y = 10, rule = aurora19plus9.A\$8.A.4A\$7.A6.A\$6.A\$5.A\$4.A\$3.A\$2.A\$.A\$A!`

Two p10
`x = 27, y = 7, rule = aurora19plus2.A\$2.A\$23.4A2\$A.A2.2A17.2A\$A\$3A20.4A!`

p20
`x = 6, y = 15, rule = aurora19plus2.2A2\$6A2\$.4A2\$6A2\$6A2\$.4A2\$6A2\$2.2A!`

edit: a smaller p10 + related p20 and a p30; a p50 from two of the 1st p10; and a color table for an auroral feel
`x = 76, y = 22, rule = aurora19plus67.A6.A2\$66.2A6.2A4\$69.4A\$3.4A25.4A\$70.2A\$4.2A27.2A2\$A8.A\$33.2A\$A8.A60.2A\$32.4A\$69.4A4\$66.2A6.2A2\$67.A6.A!`

`x = 14, y = 7, rule = aurora19plus10.4A2\$4A7.2A2\$.2A7.4A2\$4A!`

`color=0   0 0 23color=1 207 255 255color=2 175 223 255color=3 143 191 255color=4 111 159 255color=5 79 127 255color=6 0 255 63color=7 0 255 95color=8 0 255 127color=9 0 255 159`

Tropylium

Posts: 406
Joined: May 31st, 2011, 7:12 pm
Location: Finland

### Re: Mildly interesting rule

Anyway, back to Aurora 19 the original. Here's an amusing "breeder minus breeder":
`x = 9, y = 12, rule = aurora192A3\$2.2A3\$4.2A3\$6.2A\$8.A\$8.A!`

This creates two-way forerakes, initially creating two overlapping quadratically growing spaceship fields (at its clearest around 7K-8K gens). Then the two outputs start colliding though, and we're left with just an elaborate "elbowed" rake system.

Tropylium

Posts: 406
Joined: May 31st, 2011, 7:12 pm
Location: Finland

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